(i) Given, 7, 13, 19, …, 205 is the A.P

Therefore

First term, a = 7

Common difference, d = a₂ − a₁ = 13 − 7 = 6

Let there are n terms in this A.P.

a_n = 205

As we know, for an A.P.,

a_n = a + (n − 1) d

Therefore, 205 = 7 + (n − 1) 6

198 = (n − 1) 6

33 = (n − 1)

n = 34

Therefore, this given series has 34 terms in it.

(ii) 18, \(15 \frac{1}{2}\), 13..., -47

First term, a = 18

Common difference, d = a₂-a₁ = \(15 \frac{1}{2}\) 

d = (31-36)/2 = -5/2

Let there are n terms in this A.P.

a_n = 205

As we know, for an A.P.,

a_n = a+(n−1)d

-47 = 18+(n-1)(-5/2)

-47-18 = (n-1)(-5/2)

-65 = (n-1)(-5/2)

(n-1) = -130/-5

(n-1) = 26

n = 27

Therefore, this given A.P. has 27 terms in it.